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[20] The Panel effectively called for an end to the Math Wars, concluding that research showed "conceptual understanding, computational and procedural fluency, and problem-solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided."
The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving. [3]
Reform texts emphasize written and verbal communication, working in cooperative groups, and making connections between concepts and between representations. One of principles of reform mathematics is social equity. [5] In contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill-building ...
The concept of procedural knowledge is also widely used in mathematics educational researches. The well-influential definition of procedural knowledge in this domain comes from the introductory chapter by Hiebert and Lefevre (1986) of the seminal book "Conceptual and procedural knowledge: The case of mathematics", in which they divided ...
This emphasis by no means excludes the learning of number facts; indeed, a major goal of early mathematical education is procedural fluency. The NCTM in recent revisions has made more explicit this need for learning of basic math facts and correct, efficient methods. Many new editions of standards-based texts do present standard methods and ...
Curricula that support starting from conceptual understanding, then developing procedural fluency, for example, AIMS Foundation Activities, [6] frequently use multiple representations. Supporting student use of multiple representations may lead to more open-ended problems, or at least accepting multiple methods of solutions and forms of answers.
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
Foundations of mathematics are the logical and mathematical framework that allows the development of ... it is a conceptual system possessing internal necessity that ...